solidify modifier is distorting parts of the model
The fastest way to fix this is probably just to split the blade and the hilt, and apply solidify to only the blade.

To split the blade from the hilt, go into edit mode with the sword selected, then click anywhere on the blade and press ctrl+l, which will select all linked.  If this selects the hilt too, you will need to select the faces manually.  Once you have the blade isolated, press p while still in edit mode, then choose "selected".  This will break the sword object into a hilt object and blade object.  

From there, you can just apply solidify to the blade as you did before.

From a 3D printer perspective, you may want to not print the blade at all, and make it yourself with plastic sheets from Hobby-Lobby or something.  3D printers have some trouble with long and thin.  Not to mention you will save money from avoiding printing costs.